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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 4

Characterizations of a helicoid and a catenoid

Zuhal Kucukarslan Yuzbasi(FIRAT UNIVERSITY)0000-0001-7630-5490
Dae Won Yoon(Gyeongsang National University)0000-0001-8620-0676
Sayfa
—
Yayın Tarihi
2022-08-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally we show some examples of minimal surfaces generated by a circle and a helix.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present article, we consider a parametric surface generated by the Frenet frame of a curve, and study the minimality condition for the surface.
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Temel Bulgular & Veri:As a result, we give characterizations of a helicoid and a catenoid.
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Sonuç & Katkı:Finally we show some examples of minimal surfaces generated by a circle and a helix.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:minimal surface · catenoid · helicoid

Abstract

In the present article, we consider a parametric surface generated by the Frenet frame of a curve, and study the minimality condition for the surface. As a result, we give characterizations of a helicoid and a catenoid. Finally we show some examples of minimal surfaces generated by a circle and a helix.

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Bu Makaleye Atıf Yap

Yuzbasi, Z. K., Yoon, D. W. (2022). Characterizations of a helicoid and a catenoid. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 4. https://doi.org/10.15672/hujms.881876

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Kaynakça (10)

  1. Y.-X. Hao, R.-H. Wang and C.-J. Li, Minimal quasi-Bézier surface, Appl. Math. Model. 36, 5751–5757, 2012.
  2. E. Kasap and F.T. Akyildiz, Surfaces with common geodesic in Minkowski 3-space, Appl. Math. Comput. 177, 260–270, 2006.
  3. E. Kasap, F.T. Akyildiz and K. Orbay, A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput. 201, 781–789, 2008.
  4. C.-Y. Li, R.-H. Wang and C.-G. Zhu, Designing approximation minimal parametric surfaces with geodesics Appl. Math. Model. 37, 6415–6424, 2013.
  5. C.M.C. Riverros and A.M.V. Corro, Geodesics in minimal surfaces, Math. Notes, 101, 497–514, 2017.
  6. J. Sánchez-Reyes, On the construction of minimal surfaces from geodesics, Appl. Math. Model. 40, 1676–1682, 2016.
  7. J. Sánchez-Reyes and R. Dorado, Constrained design of polynomial surfaces from geodesic curves, Comput. Aided Design. 40, 49–55, 2008.
  8. G.-J. Wang, K. Tang and C.-L. Tai, Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Design. 36, 447–459, 2004.
  9. G. Xu and G.-Z. Wang, Quintic parametric polynomial minimal surfaces and thier properties, Diff. Geom. Appl. 28, 697–704, 2010.
  10. D.W. Yoon, Approximation of minimal surfaces in Minkowski 3-space, preprint.